Optimal standby activation in m‐out‐of‐n systems: A preventive approach

Abstract

This article investigates an optimal preventive standby activation policy for an m$$ m $$‐out‐of‐n$$ n $$ redundant system. We assume that for such a system, which starts operating at time t=0$$ t=0 $$, a standby component will be activated at either the failure time of the system or at a predetermined time τ$$ \tau $$, whichever occurs first. We first obtain the system reliability function under this switching policy as a function of τ$$ \tau $$. Then, we investigate the optimal switching time τ$$ \tau $$ so that the mean time to failure of the system is maximized. The results indicate that the existence of an optimal value of τ$$ \tau $$ depends on the lifetime of the standby redundancy and its virtual age in the standby state. Some illustrative examples are presented to examine the theoretical outcomes.